# How do you find the derivative for #f (x) = -3ln2x#?

Applying the chain rule:

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To find the derivative of ( f(x) = -3\ln(2x) ), you can use the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

The derivative of ( \ln(2x) ) is ( \frac{1}{2x} ). Therefore, the derivative of ( -3\ln(2x) ) is ( -3 ) times ( \frac{1}{2x} ), which simplifies to ( -\frac{3}{2x} ). So, the derivative of ( f(x) ) is ( -\frac{3}{2x} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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